Analysis and optimization of a natural draft heat sink system

An analytical solution for a system consisting of a vertical, parallel-plate, isothermal heat sink, and a chimney is presented. The result is applied to problems in which the size of the overall system is constrained. A ridge of maximum total heat transfer is observed with respect to the plate spacing and heat-sink height. The ridge suggests that heat-sink height may be reduced without diminishing the thermal performance for natural draft cooling. The flow characteristics of optimal systems reveal that systems with and without chimneys dissipate maximum heat when the velocity profiles within the heat sink are fully developed and developing, respectively.